Unlike \(V_R\)  and \(V_Z\) , the density function of \(V_\phi \)  is non-Gaussian. [1]} proposed an analytic PDF for \(V_\phi \) , which has been used in [2]} to estimate velocity moments for dwarf stars. The PDF of \(V_\phi \) , \(f(V_\varphi )\) , is written as
\(f(V_\varphi )&=&\rm {constant} \times \exp \big (-\frac{(V_\varphi -b_0)^2}{2\sigma ^{\prime 2}_\varphi }\big ),\nonumber \\\sigma ^{\prime }_\varphi &=&b_1+b_2V_{\varphi 100}+b_3V^2_{\varphi 100}+b_4V^3_{\varphi 100},\) 
